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<h1><img src="../../../../boost.png" alt="boost.png (6897 bytes)" align=
"middle" width="277" height="86">Boost.MultiIndex Hashed indices reference</h1>

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Boost.MultiIndex reference
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<h2>Contents</h2>

<ul>
  <li><a href="#hash_index_fwd_synopsis">Header
    <code>"boost/multi_index/hashed_index_fwd.hpp"</code> synopsis</a></li>
  <li><a href="#synopsis">Header
    <code>"boost/multi_index/hashed_index.hpp"</code> synopsis</a>
    <ul>
      <li><a href="#unique_non_unique">
        Index specifiers <code>hashed_unique</code> and <code>hashed_non_unique</code>
        </a></li>
      <li><a href="#hash_indices">Hashed indices</a>
        <ul>
          <li><a href="#complexity_signature">Complexity signature</a></li>
          <li><a href="#instantiation_types">Instantiation types</a></li>
          <li><a href="#types">Nested types</a></li>
          <li><a href="#constructors">Constructors, copy and assignment</a></li>
          <li><a href="#iterators">Iterators</a></li>
          <li><a href="#modifiers">Modifiers</a></li>
          <li><a href="#observers">Observers</a></li>
          <li><a href="#lookup">Lookup</a></li>
          <li><a href="#bucket_interface">Bucket interface</a></li>
          <li><a href="#hash_policy">Hash policy</a></li>
          <li><a href="#comparison">Comparison</a></li>
          <li><a href="#serialization">Serialization</a></li>
        </ul>
      </li>
    </ul>
  </li>
</ul>

<h2>
<a name="hash_index_fwd_synopsis">Header
<a href="../../../../boost/multi_index/hashed_index_fwd.hpp">
<code>"boost/multi_index/hashed_index_fwd.hpp"</code></a> synopsis</a></h2>

<blockquote><pre>
<span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

<span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

<span class=comment>// index specifiers hashed_unique and hashed_non_unique</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>consult hashed_unique reference for arguments</b><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>hashed_unique</span><span class=special>;</span>
<span class=keyword>template</span><span class=special>&lt;</span><b>consult hashed_non_unique reference for arguments</b><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>hashed_non_unique</span><span class=special>;</span>

<span class=comment>// indices</span>

<span class=keyword>namespace</span> <span class=identifier>detail</span><span class=special>{</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined</b><span class=special>&gt;</span> <span class=keyword>class</span> <b>index name is implementation defined</b><span class=special>;</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index::detail</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index</span> 

<span class=special>}</span> <span class=comment>// namespace boost</span>
</pre></blockquote>

<p>
<code>hashed_index_fwd.hpp</code> provides forward declarations for index specifiers 
<a href="#unique_non_unique"><code>hashed_unique</code> and <code>hashed_non_unique</code></a> and
their associated <a href="#hash_indices">hashed index</a> classes.
</p>

<h2>
<a name="synopsis">Header
<a href="../../../../boost/multi_index/hashed_index.hpp">
<code>"boost/multi_index/hashed_index.hpp"</code></a> synopsis</a></h2>

<blockquote><pre>
<span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>initializer_list</span><span class=special>&gt;</span>

<span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

<span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

<span class=comment>// index specifiers hashed_unique and hashed_non_unique</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>consult hashed_unique reference for arguments</b><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>hashed_unique</span><span class=special>;</span>
<span class=keyword>template</span><span class=special>&lt;</span><b>consult hashed_non_unique reference for arguments</b><span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=identifier>hashed_non_unique</span><span class=special>;</span>

<span class=comment>// indices</span>

<span class=keyword>namespace</span> <span class=identifier>detail</span><span class=special>{</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined</b><span class=special>&gt;</span> <span class=keyword>class</span> <b>index class name implementation defined</b><span class=special>;</span>

<span class=comment>// index comparison:</span>

<span class=comment>// <b>OP</b> is any of ==,!=</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span> <b><i>OP</i></b><span class=special>(</span><span class=keyword>const</span> <b>index class name</b><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <b>index class name</b><span class=special>&amp;</span> <span class=identifier>y</span><span class=special>);</span>

<span class=comment>// index specialized algorithms:</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined</b><span class=special>&gt;</span>
<span class=keyword>void</span> <span class=identifier>swap</span><span class=special>(</span><b>index class name</b><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><b>index class name</b><span class=special>&amp;</span> <span class=identifier>y</span><span class=special>);</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index::detail</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index</span> 

<span class=special>}</span> <span class=comment>// namespace boost</span>
</pre></blockquote>

<h3><a name="unique_non_unique">
Index specifiers <code>hashed_unique</code> and <code>hashed_non_unique</code>
</a></h3>

<p>
These <a href="indices.html#index_specification">index specifiers</a> allow
for insertion of <a href="#hash_indices">hashed indices</a> without and with
allowance of duplicate elements, respectively. The syntax of <code>hashed_unique</code>
and <code>hashed_non_unique</code> coincide, thus we describe them in a grouped manner.
<code>hashed_unique</code> and <code>hashed_non_unique</code> can be instantiated in
two different forms, according to whether a tag list for the index is provided or not:
</p>

<blockquote><pre>
<span class=keyword>template</span><span class=special>&lt;</span>
  <span class=keyword>typename</span> <span class=identifier>KeyFromValue</span><span class=special>,</span>
  <span class=keyword>typename</span> <span class=identifier>Hash</span><span class=special>=</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>hash</span><span class=special>&lt;</span><span class=identifier>KeyFromValue</span><span class=special>::</span><span class=identifier>result_type</span><span class=special>&gt;,</span>
  <span class=keyword>typename</span> <span class=identifier>Pred</span><span class=special>=</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>equal_to</span><span class=special>&lt;</span><span class=identifier>KeyFromValue</span><span class=special>::</span><span class=identifier>result_type</span><span class=special>&gt;</span>
<span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=special>(</span><span class=identifier>hashed_unique</span> <span class=special>|</span> <span class=identifier>hashed_non_unique</span><span class=special>)</span><span class=special>;</span>

<span class=keyword>template</span><span class=special>&lt;</span>
  <span class=keyword>typename</span> <span class=identifier>TagList</span><span class=special>,</span>
  <span class=keyword>typename</span> <span class=identifier>KeyFromValue</span><span class=special>,</span>
  <span class=keyword>typename</span> <span class=identifier>Hash</span><span class=special>=</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>hash</span><span class=special>&lt;</span><span class=identifier>KeyFromValue</span><span class=special>::</span><span class=identifier>result_type</span><span class=special>&gt;,</span>
  <span class=keyword>typename</span> <span class=identifier>Pred</span><span class=special>=</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>equal_to</span><span class=special>&lt;</span><span class=identifier>KeyFromValue</span><span class=special>::</span><span class=identifier>result_type</span><span class=special>&gt;</span>
<span class=special>&gt;</span>
<span class=keyword>struct</span> <span class=special>(</span><span class=identifier>hashed_unique</span> <span class=special>|</span> <span class=identifier>hashed_non_unique</span><span class=special>)</span><span class=special>;</span>
</pre></blockquote>

<p>
If provided, <code>TagList</code> must be an instantiation of the class template
<a href="indices.html#tag"><code>tag</code></a>.
The template arguments are used by the corresponding index implementation,
refer to the <a href="#hash_indices">hashed indices</a> reference section for further
explanations on their acceptable type values.
</p>

<h3><a name="hash_indices">Hashed indices</a></h3>

<p>
A hashed index provides fast retrieval of elements of a <code>multi_index_container</code>
through hashing techniques.
A hashed index is particularized according to a given
<a href="key_extraction.html#key_extractors"><code>Key Extractor</code></a>
that retrieves keys from elements of <code>multi_index_container</code>, a <code>Hash</code>
function object which returns hash values for the keys and a binary predicate <code>Pred</code>
acting as an equivalence relation on values of <code>Key</code>.
</p>

<p>
There are two variants of hashed indices: <i>unique</i>, which do
not allow duplicate elements (with respect to its associated equality
predicate) and <i>non-unique</i>, which accept those duplicates.
The interface of these two variants is the same, so they are documented
together, with minor differences explicitly stated when they exist.
</p>

<p>
Except where noted or if the corresponding interface does not exist, hashed indices
(both unique and non-unique) satisfy the C++ requirements for unordered associative
containers at <b>[unord.req]</b> (supporting unique and equivalent keys, respectively.)
Iterators (including to the end of the index) and pointers and references to an element
remain valid during the lifetime of the associated container (which can change
upon swapping), or until the referred-to element is erased or extracted;
pointers and references to an extracted element, but not so for iterators,
become valid again once the element is re-inserted.
Occasionally, the exception safety guarantees provided
are actually stronger than required by the standard. We only provide descriptions of
those types and operations that do not exactly conform to or are not mandated by the standard
requirements. 
</p>

<blockquote><pre>
<span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

<span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

<span class=keyword>namespace</span> <span class=identifier>detail</span><span class=special>{</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined: dependent on types Value, Allocator,
  TagList, KeyFromValue, Hash, Pred</b><span class=special>&gt;</span>
<span class=keyword>class</span> <b>name is implementation defined</b>
<span class=special>{</span> 
<span class=keyword>public</span><span class=special>:</span>
  <span class=comment>// types:</span>

  <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>KeyFromValue</span><span class=special>::</span><span class=identifier>result_type</span>         <span class=identifier>key_type</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>Value</span>                                      <span class=identifier>value_type</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>KeyFromValue</span>                               <span class=identifier>key_from_value</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>Hash</span>                                       <span class=identifier>hasher</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>Pred</span>                                       <span class=identifier>key_equal</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>tuple</span><span class=special>&lt;</span>
    <span class=identifier>size_type</span><span class=special>,</span><span class=identifier>key_from_value</span><span class=special>,</span><span class=identifier>hasher</span><span class=special>,</span><span class=identifier>key_equal</span><span class=special>&gt;</span>       <span class=identifier>ctor_args</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>TagList</span>                                    <span class=identifier>tag_list</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=identifier>Allocator</span>                                  <span class=identifier>allocator_type</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>Allocator</span><span class=special>::</span><span class=identifier>pointer</span>                <span class=identifier>pointer</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>Allocator</span><span class=special>::</span><span class=identifier>const_pointer</span>          <span class=identifier>const_pointer</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>Allocator</span><span class=special>::</span><span class=identifier>reference</span>              <span class=identifier>reference</span><span class=special>;</span>
  <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>Allocator</span><span class=special>::</span><span class=identifier>const_reference</span>        <span class=identifier>const_reference</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>size_type</span><span class=special>;</span>      
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>difference_type</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>iterator</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>const_iterator</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>local_iterator</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>implementation defined                     </b><span class=identifier>const_local_iterator</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>same as owning container                   </b><span class=identifier>node_type</span><span class=special>;</span>
  <span class=keyword>typedef</span> <b>following [container.insert.return] spec   </b><span class=identifier>insert_return_type</span><span class=special>;</span>

  <span class=comment>// construct/destroy/copy:</span>

  <b>index class name</b><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>=(</span><span class=keyword>const</span> <b>index class name</b><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <b>index class name</b><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>=(</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>initializer_list</span><span class=special>&lt;</span><span class=identifier>value_type</span><span class=special>&gt;</span> <span class=identifier>list</span><span class=special>);</span>

  <span class=identifier>allocator_type</span> <span class=identifier>get_allocator</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>

  <span class=comment>// size and capacity:</span>

  <span class=keyword>bool</span>      <span class=identifier>empty</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>size_type</span> <span class=identifier>size</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>size_type</span> <span class=identifier>max_size</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>

  <span class=comment>// iterators:</span>

  <span class=identifier>iterator</span>       <span class=identifier>begin</span><span class=special>()</span><span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_iterator</span> <span class=identifier>begin</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>iterator</span>       <span class=identifier>end</span><span class=special>()</span><span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_iterator</span> <span class=identifier>end</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>const_iterator</span> <span class=identifier>cbegin</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
  <span class=identifier>const_iterator</span> <span class=identifier>cend</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
 
  <span class=identifier>iterator</span>       <span class=identifier>iterator_to</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>const_iterator</span> <span class=identifier>iterator_to</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=comment>// modifiers:</span>


  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span><span class=special>...</span> <span class=identifier>Args</span><span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=keyword>bool</span><span class=special>&gt;</span> <span class=identifier>emplace</span><span class=special>(</span><span class=identifier>Args</span><span class=special>&amp;&amp;...</span> <span class=identifier>args</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span><span class=special>...</span> <span class=identifier>Args</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>emplace_hint</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>Args</span><span class=special>&amp;&amp;...</span> <span class=identifier>args</span><span class=special>);</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=keyword>bool</span><span class=special>&gt;</span> <span class=identifier>insert</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=keyword>bool</span><span class=special>&gt;</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>value_type</span><span class=special>&amp;&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>iterator</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>iterator</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>value_type</span><span class=special>&amp;&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>InputIterator</span><span class=special>&gt;</span>
  <span class=keyword>void</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>InputIterator</span> <span class=identifier>first</span><span class=special>,</span><span class=identifier>InputIterator</span> <span class=identifier>last</span><span class=special>);</span>
  <span class=keyword>void</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>initializer_list</span><span class=special>&lt;</span><span class=identifier>value_type</span><span class=special>&gt;</span> <span class=identifier>list</span><span class=special>);</span>
  <span class=identifier>insert_return_type</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>node_type</span><span class=special>&amp;&amp;</span> <span class=identifier>nh</span><span class=special>);</span>
  <span class=identifier>iterator</span> <span class=identifier>insert</span><span class=special>(</span><span class=identifier>const_iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>node_type</span><span class=special>&amp;&amp;</span> <span class=identifier>nh</span><span class=special>);</span>

  <span class=identifier>node_type</span> <span class=identifier>extract</span><span class=special>(</span><span class=identifier>const_iterator</span> <span class=identifier>position</span><span class=special>);</span>
  <span class=identifier>node_type</span> <span class=identifier>extract</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>key_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>

  <span class=identifier>iterator</span>  <span class=identifier>erase</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>);</span>
  <span class=identifier>size_type</span> <span class=identifier>erase</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>key_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>iterator</span>  <span class=identifier>erase</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>first</span><span class=special>,</span><span class=identifier>iterator</span> <span class=identifier>last</span><span class=special>);</span>

  <span class=keyword>bool</span> <span class=identifier>replace</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=keyword>bool</span> <span class=identifier>replace</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>value_type</span><span class=special>&amp;&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Modifier</span><span class=special>&gt;</span> <span class=keyword>bool</span> <span class=identifier>modify</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>Modifier</span> <span class=identifier>mod</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Modifier</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Rollback</span><span class=special>&gt;</span>
  <span class=keyword>bool</span> <span class=identifier>modify</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>Modifier</span> <span class=identifier>mod</span><span class=special>,</span><span class=identifier>Rollback</span> <span class=identifier>back</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Modifier</span><span class=special>&gt;</span> <span class=keyword>bool</span> <span class=identifier>modify_key</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>Modifier</span> <span class=identifier>mod</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Modifier</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Rollback</span><span class=special>&gt;</span>
  <span class=keyword>bool</span> <span class=identifier>modify_key</span><span class=special>(</span><span class=identifier>iterator</span> <span class=identifier>position</span><span class=special>,</span><span class=identifier>Modifier</span> <span class=identifier>mod</span><span class=special>,</span><span class=identifier>Rollback</span> <span class=identifier>back</span><span class=special>);</span>
  
  <span class=keyword>void</span> <span class=identifier>clear</span><span class=special>()</span><span class=keyword>noexcept</span><span class=special>;</span>
  <span class=keyword>void</span> <span class=identifier>swap</span><span class=special>(</span><b>index class name</b><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Index</span><span class=special>&gt;</span> <span class=keyword>void</span> <span class=identifier>merge</span><span class=special>(</span><span class=identifier>Index</span><span class=special>&amp;&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Index</span><span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=keyword>bool</span><span class=special>&gt;</span> <span class=identifier>merge</span><span class=special>(</span>
    <span class=identifier>Index</span><span class=special>&amp;&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>remove_reference_t</span><span class=special>&lt;</span><span class=identifier>Index</span><span class=special>&gt;::</span><span class=identifier>const_iterator</span> <span class=identifier>i</span><span class=special>);</span>
  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Index</span><span class=special>&gt;</span>
  <span class=keyword>void</span> <span class=identifier>merge</span><span class=special>(</span>
    <span class=identifier>Index</span><span class=special>&amp;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
    <span class=keyword>typename</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>remove_reference_t</span><span class=special>&lt;</span><span class=identifier>Index</span><span class=special>&gt;::</span><span class=identifier>const_iterator</span> <span class=identifier>first</span><span class=special>,</span>
    <span class=keyword>typename</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>remove_reference_t</span><span class=special>&lt;</span><span class=identifier>Index</span><span class=special>&gt;::</span><span class=identifier>const_iterator</span> <span class=identifier>last</span><span class=special>);</span>

  <span class=comment>// observers:</span>

  <span class=identifier>key_from_value</span> <span class=identifier>key_extractor</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
  <span class=identifier>hasher</span>         <span class=identifier>hash_function</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
  <span class=identifier>key_equal</span>      <span class=identifier>key_eq</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>

  <span class=comment>// lookup:</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>find</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span>
    <span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleHash</span><span class=special>,</span> <span class=keyword>typename</span> <span class=identifier>CompatiblePred</span>
  <span class=special>&gt;</span>
  <span class=identifier>iterator</span> <span class=identifier>find</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleHash</span><span class=special>&amp;</span> <span class=identifier>hash</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatiblePred</span><span class=special>&amp;</span> <span class=identifier>eq</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span> 

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>size_type</span> <span class=identifier>count</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span>
    <span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleHash</span><span class=special>,</span> <span class=keyword>typename</span> <span class=identifier>CompatiblePred</span>
  <span class=special>&gt;</span>
  <span class=identifier>size_type</span> <span class=identifier>count</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleHash</span><span class=special>&amp;</span> <span class=identifier>hash</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatiblePred</span><span class=special>&amp;</span> <span class=identifier>eq</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=keyword>bool</span> <span class=identifier>contains</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span>
    <span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleHash</span><span class=special>,</span> <span class=keyword>typename</span> <span class=identifier>CompatiblePred</span>
  <span class=special>&gt;</span>
  <span class=keyword>bool</span> <span class=identifier>contains</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleHash</span><span class=special>&amp;</span> <span class=identifier>hash</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatiblePred</span><span class=special>&amp;</span> <span class=identifier>eq</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=identifier>iterator</span><span class=special>&gt;</span> <span class=identifier>equal_range</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=keyword>template</span><span class=special>&lt;</span>
    <span class=keyword>typename</span> <span class=identifier>CompatibleKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompatibleHash</span><span class=special>,</span> <span class=keyword>typename</span> <span class=identifier>CompatiblePred</span>
  <span class=special>&gt;</span>
  <span class=identifier>std</span><span class=special>::</span><span class=identifier>pair</span><span class=special>&lt;</span><span class=identifier>iterator</span><span class=special>,</span><span class=identifier>iterator</span><span class=special>&gt;</span> <span class=identifier>equal_range</span><span class=special>(</span>
    <span class=keyword>const</span> <span class=identifier>CompatibleKey</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,
    </span><span class=keyword>const</span> <span class=identifier>CompatibleHash</span><span class=special>&amp;</span> <span class=identifier>hash</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>CompatiblePred</span><span class=special>&amp;</span> <span class=identifier>eq</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=comment>// bucket interface:</span>

  <span class=identifier>size_type</span> <span class=identifier>bucket_count</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>size_type</span> <span class=identifier>max_bucket_count</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=identifier>size_type</span> <span class=identifier>bucket_size</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=identifier>size_type</span> <span class=identifier>bucket</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>key_type</span><span class=special>&amp;</span> <span class=identifier>k</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=identifier>local_iterator</span>       <span class=identifier>begin</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>);</span>
  <span class=identifier>const_local_iterator</span> <span class=identifier>begin</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=identifier>local_iterator</span>       <span class=identifier>end</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>);</span>
  <span class=identifier>const_local_iterator</span> <span class=identifier>end</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=identifier>const_local_iterator</span> <span class=identifier>cbegin</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
  <span class=identifier>const_local_iterator</span> <span class=identifier>cend</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=identifier>local_iterator</span>       <span class=identifier>local_iterator_to</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>
  <span class=identifier>const_local_iterator</span> <span class=identifier>local_iterator_to</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

  <span class=comment>// hash policy:</span>

  <span class=keyword>float</span> <span class=identifier>load_factor</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=keyword>float</span> <span class=identifier>max_load_factor</span><span class=special>()</span><span class=keyword>const</span> <span class=keyword>noexcept</span><span class=special>;</span>
  <span class=keyword>void</span>  <span class=identifier>max_load_factor</span><span class=special>(</span><span class=keyword>float</span> <span class=identifier>z</span><span class=special>);</span>
  <span class=keyword>void</span>  <span class=identifier>rehash</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>);</span>
  <span class=keyword>void</span>  <span class=identifier>reserve</span><span class=special>(</span><span class=identifier>size_type</span> <span class=identifier>n</span><span class=special>);</span>
<span class=special>};</span>

<span class=comment>// index comparison:</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>==(</span><span class=keyword>const</span> <b>index class name</b><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <b>index class name</b><span class=special>&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=special>;</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined</b><span class=special>&gt;</span>
<span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>!=(</span><span class=keyword>const</span> <b>index class name</b><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <b>index class name</b><span class=special>&amp;</span> <span class=identifier>y</span><span class=special>)</span>
<span class=special>{</span>
  <span class=keyword>return</span> <span class=special>!(</span><span class=identifier>x</span><span class=special>==</span><span class=identifier>y</span><span class=special>);</span>
<span class=special>}</span>

<span class=comment>// index specialized algorithms:</span>

<span class=keyword>template</span><span class=special>&lt;</span><b>implementation defined</b><span class=special>&gt;</span>
<span class=keyword>void</span> <span class=identifier>swap</span><span class=special>(</span><b>index class name</b><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><b>index class name</b><span class=special>&amp;</span> <span class=identifier>y</span><span class=special>);</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index::detail</span>

<span class=special>}</span> <span class=comment>// namespace boost::multi_index</span> 

<span class=special>}</span> <span class=comment>// namespace boost</span>
</pre></blockquote>

<h4><a name="complexity_signature">Complexity signature</a></h4>

<p>
Here and in the descriptions of operations of hashed indices, we adopt the
scheme outlined in the 
<a href="indices.html#complexity_signature">complexity signature
section</a>. The complexity signature of hashed indices is:
<ul>
  <li>copying: <code>c(n)=n*log(n)</code>,</li>
  <li>insertion: average case <code>i(n)=1</code> (amortized constant),
    worst case <code>i(n)=n<sub>dist</sub></code>,</li>
  <li>hinted insertion: average case <code>h(n)=1</code> (amortized constant),
    worst case <code>h(n)=n<sub>dist</sub></code>,</li>
  <li>deletion: <code>d(n)=1</code> (constant),</li>
  <li>replacement:
    <ul>
      <li>if the new element key is equivalent to the original, <code>r(n)=1</code> (constant),</li>
      <li>otherwise, average case <code>r(n)=1</code> (constant),
        worst case <code>r(n)=n<sub>dist</sub></code>,</li>
    </ul></li>
  <li>modifying: average case <code>m(n)=1</code> (constant),
    worst case <code>m(n)=n<sub>dist</sub></code>,</li>
</ul>
where <code>n<sub>dist</sub></code> is the number of non-equivalent elements out of
the total <code>n</code>.
</p>

<h4><a name="instantiation_types">Instantiation types</a></h4>

<p>Hashed indices are instantiated internally to <code>multi_index_container</code> and
specified by means of <a href="indices.html#indexed_by"><code>indexed_by</code></a>
with <a href="#unique_non_unique"> index specifiers <code>hashed_unique</code>
and <code>hashed_non_unique</code></a>. Instantiations are dependent on the
following types:
<ul>
  <li><code>Value</code> from <code>multi_index_container</code>,</li>
  <li><code>Allocator</code> from <code>multi_index_container</code>,</li>
  <li><code>TagList</code> from the index specifier (if provided, otherwise <code>tag&lt;&gt;</code> is assumed),</li>
  <li><code>KeyFromValue</code> from the index specifier,</li>
  <li><code>Hash</code> from the index specifier,</li>
  <li><code>Pred</code> from the index specifier.</li>
</ul>
<code>TagList</code> must be an instantiation of
<a href="indices.html#tag"><code>tag</code></a>. The type <code>KeyFromValue</code>,
which determines the mechanism for extracting a key from <code>Value</code>,
must be a model of <a href="key_extraction.html#key_extractors">
<code>Key Extractor</code></a> from <code>Value</code>. <code>Hash</code> is a
<code>CopyConstructible</code>unary function object 
taking a single argument of type <code>KeyFromValue::result_type</code> and returning a
value of type <code>std::size_t</code> in the range
<code>[0, std::numeric_limits&lt;std::size_t&gt;::max())</code>.
<code>Pred</code> is a <code>CopyConstructible</code> binary predicate inducing an equivalence relation
on elements of <code>KeyFromValue::result_type</code>. It is required that
the <code>Hash</code> object return the same value for keys
equivalent under <code>Pred</code>.
</p>

<h4><a name="types">Nested types</a></h4>

<code>ctor_args</code>

<blockquote>
The first element of this tuple indicates the minimum number of buckets
set up by the index on construction time. If the default value 0 is used,
an implementation defined number is used instead.
</blockquote>

<code>iterator<br>
const_iterator<br>
local_iterator<br>
const_local_iterator</code>

<blockquote>
These types are forward iterators. They depend only on <code>node_type</code>,
the position of the index in the <code>multi_index_container</code>, and whether
the index is unique or not (this implies that, for instance, iterators to elements transferred
from a unique index to a non-unique one will become invalid).
</blockquote>

<h4><a name="constructors">Constructors, copy and assignment</a></h4>

<p>
As explained in the <a href="indices.html#index_concepts">index
concepts section</a>, indices do not have public constructors or destructors.
Assignment, on the other hand, is provided. Upon construction,
<code>max_load_factor()</code> is 1.0.
</p>

<code><b>index class name</b>&amp; operator=(const <b>index class name</b>&amp; x);</code>

<blockquote>
<b>Effects:</b>
<blockquote><pre>
<span class=identifier>a</span><span class=special>=</span><span class=identifier>b</span><span class=special>;</span>
</pre></blockquote>
where <code>a</code> and <code>b</code> are the <code>multi_index_container</code>
objects to which <code>*this</code> and <code>x</code> belong, respectively.<br>
<b>Returns:</b> <code>*this</code>.<br>
</blockquote>

<code><b>index class name</b>&amp; operator=(std::initializer_list&lt;value_type&gt; list);</code>

<blockquote>
<b>Effects:</b>
<blockquote><pre>
<span class=identifier>a</span><span class=special>=</span><span class=identifier>list</span><span class=special>;</span>
</pre></blockquote>
where <code>a</code> is the <code>multi_index_container</code>
object to which <code>*this</code> belongs.<br>
<b>Returns:</b> <code>*this</code>.<br>
</blockquote>

<h4><a name="iterators">Iterators</a></h4>

<code>iterator&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;iterator_to(const value_type&amp; x);<br>
const_iterator iterator_to(const value_type&amp; x)const;</code>
  
<blockquote>
<b>Requires:</b> <code>x</code> is a reference to an element of the container.<br>
<b>Returns:</b> An iterator to <code>x</code>.<br>
<b>Complexity:</b> Constant.<br>
<b>Exception safety:</b> <code>nothrow</code>.<br>
</blockquote>

<h4><a name="modifiers">Modifiers</a></h4>

<code>template&lt;typename... Args&gt;<br>
std::pair&lt;iterator,bool&gt; emplace(Args&amp;&amp;... args);</code>

<blockquote>
<b>Requires:</b> <code>value_type</code> is <code>EmplaceConstructible</code>
into <code>multi_index_container</code> from <code>args</code>.<br>
<b>Effects:</b> Inserts a <code>value_type</code> object constructed with
<code>std::forward&lt;Args&gt;(args)...</code> into the <code>multi_index_container</code> to which
the index belongs if
<ul>
  <li>the index is non-unique OR no other element exists with
    equivalent key,</li>
  <li>AND insertion is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
<b>Returns:</b> The return value is a pair <code>p</code>. <code>p.second</code>
is <code>true</code> if and only if insertion took place. On successful insertion,
<code>p.first</code> points to the element inserted; otherwise, <code>p.first</code>
points to an element that caused the insertion to be banned. Note that more than
one element can be causing insertion not to be allowed.<br>
<b>Complexity:</b> <code>O(I(n))</code>.<br>
<b>Exception safety:</b> Strong, except that rehashing may occur even if the operation fails.<br>
</blockquote>

<code>template&lt;typename... Args&gt;<br>
iterator emplace_hint(iterator position, Args&amp;&amp;... args);</code>

<blockquote>
<b>Requires:</b> <code>value_type</code> is <code>EmplaceConstructible</code>
into <code>multi_index_container</code> from <code>args</code>.
<code>position</code> is a valid iterator of the index.<br>
<b>Effects:</b> Inserts a <code>value_type</code> object constructed with
<code>std::forward&lt;Args&gt;(args)...</code> into the <code>multi_index_container</code> to which
the index belongs if
<ul>
  <li>the index is non-unique OR no other element exists with
    equivalent key,</li>
  <li>AND insertion is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
<code>position</code> is used as a hint to improve the efficiency of the
operation.<br>
<b>Returns:</b> On successful insertion, an iterator to the newly inserted
element. Otherwise, an iterator to an element that caused the insertion to be
banned. Note that more than one element can be causing insertion not to be
allowed.<br>
<b>Complexity:</b> <code>O(H(n))</code>.<br>
<b>Exception safety:</b> Strong, except that rehashing may occur even if the operation fails.<br>
</blockquote>

<code>std::pair&lt;iterator,bool> insert(const value_type&amp; x);</code><br>
<code>std::pair&lt;iterator,bool> insert(value_type&amp;&amp; x);</code>

<blockquote>
<b>Requires (first version):</b> <code>value_type</code> is <code>CopyInsertable</code>
into <code>multi_index_container</code>.<br>
<b>Requires (second version):</b> <code>value_type</code> is <code>MoveInsertable</code>
into <code>multi_index_container</code>.<br>
<b>Effects:</b> Inserts <code>x</code> into the <code>multi_index_container</code> to which
the index belongs if
<ul>
  <li>the index is non-unique OR no other element exists with
    equivalent key,</li>
  <li>AND insertion is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
<b>Returns:</b> The return value is a pair <code>p</code>. <code>p.second</code>
is <code>true</code> if and only if insertion took place. On successful insertion,
<code>p.first</code> points to the element inserted; otherwise, <code>p.first</code>
points to an element that caused the insertion to be banned. Note that more than
one element can be causing insertion not to be allowed.<br>
<b>Complexity:</b> <code>O(I(n))</code>.<br>
<b>Exception safety:</b> Strong, except that rehashing may occur even if the operation fails.<br>
</blockquote>

<code>iterator insert(iterator position,const value_type&amp; x);</code><br>
<code>iterator insert(iterator position,value_type&amp;&amp; x);</code>

<blockquote>
<b>Requires (first version):</b> <code>value_type</code> is <code>CopyInsertable</code>
into <code>multi_index_container</code>.
<code>position</code> is a valid iterator of the index.<br>
<b>Requires (second version):</b> <code>value_type</code> is <code>MoveInsertable</code>
into <code>multi_index_container</code>.
<code>position</code> is a valid iterator of the index.<br>
<b>Effects:</b> Inserts <code>x</code> into the <code>multi_index_container</code> to which
the index belongs if
<ul>
  <li>the index is non-unique OR no other element exists with
    equivalent key,</li>
  <li>AND insertion is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
<code>position</code> is used as a hint to improve the efficiency of the
operation.<br>
<b>Returns:</b> On successful insertion, an iterator to the newly inserted
element. Otherwise, an iterator to an element that caused the insertion to be
banned. Note that more than one element can be causing insertion not to be
allowed.<br>
<b>Complexity:</b> <code>O(H(n))</code>.<br>
<b>Exception safety:</b> Strong, except that rehashing may occur even if the operation fails.<br>
</blockquote>

<code>template&lt;typename InputIterator><br>
void insert(InputIterator first,InputIterator last);</code>

<blockquote>
<b>Requires:</b> <code>InputIterator</code> is an input iterator.
<code>value_type</code> is
<code>EmplaceConstructible</code> into
<code>multi_index_container</code> from <code>*first</code>.
<code>first</code> and <code>last</code> are not iterators into any
index of the <code>multi_index_container</code> to which this index belongs.
<code>last</code> is reachable from <code>first</code>.<br>
<b>Effects:</b>
For each element of [<code>first</code>, <code>last</code>), in this
order, inserts it into the <code>multi_index_container</code>
to which this index belongs if
<ul>
  <li>the index is non-unique OR no other element exists with
    equivalent key,</li>
  <li>AND insertion is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
<b>Complexity:</b> <code>O(m*I(n+m))</code>, where
<code>m</code> is the number of elements in [<code>first</code>,
<code>last</code>).<br>
<b>Exception safety:</b> Basic.<br>
</blockquote>

<code>void insert(std::initializer_list&lt;value_type&gt; list);</code>

<blockquote>
<b>Effects:</b>
<blockquote><pre>
<span class=identifier>insert</span><span class=special>(</span><span class=identifier>list</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>list</span><span class=special>.</span><span class=identifier>end</span><span class=special>())</span><span class=special>;</span>
</pre></blockquote>
</blockquote>
    
<code>insert_return_type insert(node_type&amp;&amp; nh);</code>

<blockquote>
<b>Requires:</b> <code>nh.empty() || get_allocator()==nh.get_allocator()</code>.<br>
<b>Effects:</b> Does nothing if <code>nh</code> is empty; otherwise,
inserts the node owned by <code>nh</code> into the
<code>multi_index_container</code> to which the index belongs if
<ul>
  <li>the index is non-unique OR no other element exists with
    equivalent key,</li>
  <li>AND insertion is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
<b>Postconditions:</b> <code>nh</code> is empty.<br>
<b>Returns:</b> A value <code>p</code> of type <code>insert_return_type</code>.
If <code>nh</code> is empty, <code>p.position</code> is <code>end()</code>,
<code>p.inserted</code> is <code>false</code> and <code>p.node</code> is empty;
on successful insertion, <code>p.position</code> points to the element inserted,
<code>p.inserted</code> is <code>true</code> and <code>p.node</code>
is empty;
if the insertion failed, <code>p.position</code> points to an element that caused
the insertion to be banned, <code>p.inserted</code> is <code>false</code> and
<code>p.node</code> owns the original node.
Note that more than one element can be causing insertion not to be allowed.<br>
<b>Complexity:</b> <code>O(I(n))</code>.<br>
<b>Exception safety:</b> Strong, except that rehashing may occur even if the
operation fails. If an exception is thrown, <code>nh</code> is not changed.<br>
</blockquote>

<code>iterator insert(const_iterator position,node_type&amp;&amp; nh);</code>

<blockquote>
<b>Requires:</b> <code>nh.empty() || get_allocator()==nh.get_allocator()</code>.
 <code>position</code> is a valid iterator of the index.<br>
<b>Effects:</b> Does nothing if <code>nh</code> is empty; otherwise,
inserts the node owned by <code>nh</code> into the
<code>multi_index_container</code> to which the index belongs if
<ul>
  <li>the index is non-unique OR no other element exists with
    equivalent key,</li>
  <li>AND insertion is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
<code>position</code> is used as a hint to improve the efficiency of the
operation.<br>
<b>Postconditions:</b> <code>nh</code> is empty if insertion succeeds,
and is not changed otherwise.<br>
<b>Returns:</b> <code>end()</code> if <code>nh</code> is empty.
On successful insertion, an iterator to the newly inserted
element; otherwise, an iterator to an element that caused the insertion to be
banned. Note that more than one element can be causing insertion not to be
allowed.<br>
<b>Complexity:</b> <code>O(H(n))</code>.<br>
<b>Exception safety:</b> Strong, except that rehashing may occur even if the
operation fails.
If an exception is thrown, <code>nh</code> is not changed.<br>
</blockquote>

<code>node_type extract(const_iterator position);</code>

<blockquote>
<b>Requires:</b> <code>position</code> is a valid dereferenceable iterator
of the index.<br>
<b>Effects:</b> Extracts the node of the element pointed to by <code>position</code>.<br>
<b>Returns:</b> A node handle owning the extracted node.<br>
<b>Complexity:</b> <code>O(D(n))</code>.<br>
<b>Exception safety:</b> <code>nothrow</code>.<br>
</blockquote>

<code>node_type extract(const key_type&amp; x);</code>

<blockquote>
<b>Effects:</b> Extracts the node of the first element
with key equivalent to <code>x</code>, if there is any.<br>
<b>Returns:</b> A node handle owning the extracted node, or empty otherwise.<br>
<b>Complexity:</b> Average case <code>O(1 + D(n))</code>, worst case
<code>O(n<sub>dist</sub> + D(n))</code>.<br>
<b>Exception safety:</b> Strong.<br>
</blockquote>

<code>iterator erase(iterator position);</code>

<blockquote>
<b>Requires:</b> <code>position</code> is a valid dereferenceable  iterator
of the index.<br>
<b>Effects:</b> Deletes the element pointed to by <code>position</code>.<br>
<b>Returns:</b> An iterator pointing to the element immediately following
the one that was deleted, or <code>end()</code>
if no such element exists.<br>
<b>Complexity:</b> <code>O(D(n))</code>.<br>
<b>Exception safety:</b> <code>nothrow</code>.<br>
</blockquote>

<code>size_type erase(const key_type&amp; x);</code>

<blockquote>
<b>Effects:</b> Deletes the elements with key equivalent to <code>x</code>.<br>
<b>Returns:</b> Number of elements deleted.<br>
<b>Complexity:</b> Average case <code>O(1 + m*D(n))</code>, worst case
<code>O(n<sub>dist</sub> + m*D(n))</code>, where <code>m</code> is
the number of elements deleted.<br>
<b>Exception safety:</b> Basic.<br>
</blockquote>

<code>iterator erase(iterator first,iterator last);</code>

<blockquote>
<b>Requires:</b> [<code>first</code>,<code>last</code>) is a valid
range of the index.<br>
<b>Effects:</b> Deletes the elements in [<code>first</code>,<code>last</code>).<br>
<b>Returns:</b> <code>last</code>.<br>
<b>Complexity:</b> <code>O(m*D(n))</code>, where <code>m</code> is
the number of elements in [<code>first</code>,<code>last</code>).<br>
<b>Exception safety:</b> <code>nothrow</code>.<br>
</blockquote>

<a name="replace"><code>bool replace(iterator position,const value_type&amp; x);</code></a><br>
<code>bool replace(iterator position,value_type&amp;&amp; x);</code>

<blockquote>
<b>Requires (first version):</b> <code>value_type</code> is <code>CopyAssignable</code>.
<code>position</code> is a valid dereferenceable iterator of the index.<br>
<b>Requires (second version):</b> <code>value_type</code> is <code>MoveAssignable</code>.
<code>position</code> is a valid dereferenceable iterator of the index.<br>
<b>Effects:</b> Assigns the value <code>x</code> to the element pointed
to by <code>position</code> into the <code>multi_index_container</code> to which
the index belongs if, for the value <code>x</code>
<ul>
  <li>the index is non-unique OR no other element exists
    (except possibly <code>*position</code>) with equivalent key,</li>
  <li>AND replacing is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
<b>Postconditions:</b> Validity of <code>position</code> is preserved
in all cases. If the key of the new value is equivalent to that of the replaced value,
the position of the element does not change.<br>
<b>Returns:</b> <code>true</code> if the replacement took place,
<code>false</code> otherwise.<br>
<b>Complexity:</b> <code>O(R(n))</code>.<br>
<b>Exception safety:</b> Strong. If an exception is thrown by some
user-provided operation the <code>multi_index_container</code> to which the index
belongs remains in its original state.
</blockquote>
  
<a name="modify">
<code>template&lt;typename Modifier> bool modify(iterator position,Modifier mod);</code></a>

<blockquote>
<b>Requires:</b> <code>mod</code> is a unary function object
accepting arguments of type
<code>value_type&amp;</code>. <code>position</code> is a valid dereferenceable
iterator of the index.
The execution of <code>mod(e)</code>, where <code>e</code> is the element
pointed to by <code>position</code>, does not invoke any operation of the
<code>multi_index_container</code> after <code>e</code> is directly modified
or, before modification, if the operation would invalidate <code>position</code>.<br>
<b>Effects:</b> Calls <code>mod(e)</code> where <code>e</code> is the element
pointed to by <code>position</code> and rearranges <code>*position</code> into
all the indices of the <code>multi_index_container</code>. Rearrangement is successful if
<ul>
  <li>the index is non-unique OR no other element exists
    with  equivalent key,</li>
  <li>AND rearrangement is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
If the rearrangement fails, the element is erased.<br>
<b>Postconditions:</b> Validity of <code>position</code> is preserved if the
operation succeeds. If the key of the modified value is equivalent to that of the
original value, the position of the element does not change.<br>
<b>Returns:</b> <code>true</code> if the operation succeeded, <code>false</code>
otherwise.<br>
<b>Complexity:</b> <code>O(M(n))</code>.<br>
<b>Exception safety:</b> Basic. If an exception is thrown by some
user-provided operation (including <code>mod</code>), then
the element pointed to by <code>position</code> is erased.
</blockquote>

<code>template&lt;typename Modifier,typename Rollback><br>
bool modify(iterator position,Modifier mod,Rollback back);</code>

<blockquote>
<b>Requires:</b> <code>mod</code> and <code>back</code> are unary function
objects accepting arguments of type
<code>value_type&amp;</code>. <code>position</code> is a valid dereferenceable
iterator of the index.
The execution of <code>mod(e)</code>, where <code>e</code> is the element
pointed to by <code>position</code>, does not invoke any operation of the
<code>multi_index_container</code> after <code>e</code> is directly modified
or, before modification, if the operation would invalidate <code>position</code>.
<code>back(e)</code> does not invoke any operation of the
<code>multi_index_container</code>.<br>
<b>Effects:</b> Calls <code>mod(e)</code> where <code>e</code> is the element
pointed to by <code>position</code> and tries to rearrange <code>*position</code> into
all the indices of the <code>multi_index_container</code>. Rearrangement is successful if
<ul>
  <li>the index is non-unique OR no other element exists
    with  equivalent key,</li>
  <li>AND rearrangement is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
If the rearrangement fails, <code>back(e)</code> is invoked: if the resulting value
of <code>e</code> is consistent with its original position and constraints in all
indices, the element is kept, otherwise it is erased.<br>
<b>Postconditions:</b> Validity of <code>position</code> is preserved except if
the element is erased under the conditions described below.
If the key of the modified value is equivalent to that of the
original value, the position of the element does not change.<br>
<b>Returns:</b> <code>true</code> if the operation succeeded, <code>false</code>
otherwise.<br>
<b>Complexity:</b> <code>O(M(n))</code>.<br>
<b>Exception safety:</b> Strong, except if <code>mod</code> or <code>back</code> throw an
exception or <code>back(e)</code> fails to properly restore the element or there is
a throwing user-provided operation after invoking <code>back(e)</code>, in which cases
the modified element is erased. If <code>back</code>
throws inside the handling code executing after some other user-provided
operation has thrown, it is the exception generated by <code>back</code> that
is rethrown.
</blockquote>

<a name="modify_key">    
<code>template&lt;typename Modifier> bool modify_key(iterator position,Modifier mod);</code></a>

<blockquote>
<b>Requires:</b> <code>key_from_value</code> is a read/write
<a href="key_extraction.html#key_extractors"><code>Key Extractor</code></a>
from <code>value_type</code>. <code>mod</code> is a
unary function object accepting arguments of type
<code>key_type&amp;</code>. <code>position</code> is a valid dereferenceable
iterator of the index.
The execution of <code>mod(k)</code>, where <code>k</code> is the key of the element
pointed to by <code>position</code>, does not invoke any operation of the
<code>multi_index_container</code> after <code>k</code> is directly modified
or, before modification, if the operation would invalidate <code>position</code>.<br>
<b>Effects:</b> Equivalent to <code>modify(position,mod')</code>,
with <code>mod'</code> defined in such a way that
<code>mod'(x)</code> is the same as <code>mod(key(x))</code>, where
<code>key</code> is the internal <code>KeyFromValue</code> object of the index.
</blockquote>

<code>template&lt;typename Modifier,typename Rollback><br>
bool modify_key(iterator position,Modifier mod,Rollback back);</code>

<blockquote>
<b>Requires:</b> <code>key_from_value</code> is a read/write
<a href="key_extraction.html#key_extractors"><code>Key Extractor</code></a>
from <code>value_type</code>. <code>mod</code> and <code>back</code>
are unary function objects accepting arguments of type
<code>key_type&amp;</code>. <code>position</code> is a valid dereferenceable
iterator of the index.
The execution of <code>mod(k)</code>, where <code>k</code> is the key of the element
pointed to by <code>position</code>, does not invoke any operation of the
<code>multi_index_container</code> after <code>k</code> is directly modified
or, before modification, if the operation would invalidate <code>position</code>.
<code>back(k)</code> does not invoke any operation of the
<code>multi_index_container</code>.<br>
<b>Effects:</b> Equivalent to <code>modify(position,mod',back')</code>,
with <code>mod'</code> and <code>back</code> defined in such a way that
<code>mod'(x)</code> is the same as <code>mod(key(x))</code> and
<code>back'(x)</code> is the same as <code>back(key(x))</code>, where
<code>key</code> is the internal <code>KeyFromValue</code> object of the index.
</blockquote>

<code>template&lt;typename Index&gt; void merge(Index&amp;&amp; x);</code>

<blockquote>
<b>Requires:</b> <code>x</code> is a non-const reference to an index of a
<a href="multi_index_container.html#node_type">node-compatible</a>
<code>multi_index_container</code>. <code>get_allocator()==x.get_allocator()</code>.<br>
<b>Effects:</b> 
<blockquote><pre>
<span class=identifier>merge</span><span class=special>(</span><span class=identifier>x</span><span class=special>,</span><span class=identifier>x</span><span class=special>.</span><span class=identifier>begin</span><span class=special>(),</span><span class=identifier>x</span><span class=special>.</span><span class=identifier>end</span><span class=special>());</span>
</pre></blockquote>
</blockquote>

<code>
template&lt;typename Index&gt; std::pair&lt;iterator,bool&gt; merge(<br>
&nbsp;&nbsp;Index&amp;&amp; x,typename std::remove_reference_t&lt;Index&gt;::const_iterator i);
</code>

<blockquote>
<b>Requires:</b> <code>x</code> is a non-const reference to an index of a
<a href="multi_index_container.html#node_type">node-compatible</a>
<code>multi_index_container</code>. <code>get_allocator()==x.get_allocator()</code>.
<code>i</code> is a valid dereferenceable iterator of <code>x</code>.<br>
<b>Effects:</b> Does nothing if the source and destination containers are the same;
otherwise, transfers the node of the element referred to by <code>i</code> into the
<code>multi_index_container</code> to which the destination index belongs if
<ul>
  <li>the index is non-unique OR no other element exists with
    equivalent key,</li>
  <li>AND insertion is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
Note that no element is copied or destroyed in the process.<br>
<b>Postconditions:</b> If transfer succeeds, for any index in the source container
having the same <code>iterator</code>/<code>const_iterator</code> types as the corresponding
index in the destination container, iterators referring to <code>*i</code>
remain valid and behave as iterators of the destination index.<br>
<b>Returns:</b> The return value is a pair <code>p</code>. <code>p.second</code>
is <code>true</code> if and only if transfer took place or the source and destination
containers are the same. If <code>p.second</code> is <code>true</code>,
<code>p.first</code> points to <code>*i</code>; otherwise, <code>p.first</code>
points to an element that caused the insertion to be banned. Note that more than
one element can be causing insertion not to be allowed.<br>
<b>Complexity:</b> If the source and destination containers are the same,
constant; otherwise, <code>O(I(n)+D(x.size()))</code>.<br>
<b>Exception safety:</b> If the source and destination containers are the same,
<code>nothrow</code>; otherwise strong.
</blockquote>

<code>
template&lt;typename Index&gt; void merge(<br>
&nbsp;&nbsp;Index&amp;&amp; x,<br>
&nbsp;&nbsp;typename std::remove_reference_t&lt;Index&gt;::const_iterator first,<br>
&nbsp;&nbsp;typename std::remove_reference_t&lt;Index&gt;::const_iterator last);
</code>

<blockquote>
<b>Requires:</b> <code>x</code> is a non-const reference to an index of a
<a href="multi_index_container.html#node_type">node-compatible</a>
<code>multi_index_container</code>. <code>get_allocator()==x.get_allocator()</code>.
[<code>first</code>,<code>last</code>) is a valid range of <code>x</code>.<br>
<b>Effects:</b> Does nothing if the source and destination containers are the same;
otherwise, for each node in [<code>first</code>,<code>last</code>), in this order,
the node is transferred to the <code>multi_index_container</code> to which the
destination index belongs if
<ul>
  <li>the index is non-unique OR no other element exists with
    equivalent key,</li>
  <li>AND insertion is allowed by all other indices of the
    <code>multi_index_container</code>.</li>
</ul>
Note that no element is copied or destroyed in the process.<br>
<b>Postconditions:</b> For any index in the source container having the same
<code>iterator</code>/<code>const_iterator</code> types as the corresponding
index in the destination container, iterators referring to the transferred elements
remain valid and behave as iterators of the destination index.<br>
<b>Complexity:</b> If the source and destination containers are the same,
constant; otherwise, <code>O(m*(I(n+m)+D(x.size())))</code>, where
<code>m</code> is the number of elements in [<code>first</code>,
<code>last</code>).<br>
<b>Exception safety:</b> If the source and destination containers are the same,
<code>nothrow</code>; otherwise basic.
</blockquote>
    
<h4><a name="observers">Observers</a></h4>

<p>Apart from standard <code>hash_function</code> and <code>key_eq</code>,
hashed indices have a member function for retrieving the internal key extractor
used.
</p>

<code>key_from_value key_extractor()const;</code>

<blockquote>
Returns a copy of the <code>key_from_value</code> object used to construct
the index.<br>
<b>Complexity:</b> Constant.
</blockquote>

<h4><a name="lookup">Lookup</a></h4>

<p>
Hashed indices provide the full lookup functionality required by
<b>[unord.req]</b>, namely <code>find</code>,
<code>count</code>, and <code>equal_range</code>. Additionally,
these member functions are templatized to allow for non-standard
arguments, so extending the types of search operations allowed.
The kind of arguments permissible when invoking the lookup member
functions is defined by the following concept.
</p>

<p>
Consider a pair (<code>Hash</code>, <code>Pred</code>) where
<code>Hash</code> is a hash functor over values of type <code>Key</code>
and <code>Pred</code> is a binary predicate
inducing an equivalence relation
on <code>Key</code>, with the additional constraint that equivalent
keys have the same hash value.
A triplet of types (<code>CompatibleKey</code>, <code>CompatibleHash</code>,
<code>CompatiblePred</code>) is said to be a <i>compatible extension</i>
of (<code>Hash</code>, <code>Pred</code>) if
<ol>
  <li><code>CompatibleHash</code> is a hash functor on values of
    type <code>CompatibleKey</code>,</li>
  <li><code>CompatiblePred</code> is a binary predicate over (<code>Key</code>,
    <code>CompatibleKey</code>),</li>
  <li><code>CompatiblePred</code> is a binary predicate over (<code>CompatibleKey</code>,
    <code>Key</code>),</li>
  <li>if <code>c_eq(ck,k1)</code> then <code>c_eq(k1,ck)</code>,</li>
  <li>if <code>c_eq(ck,k1)</code> and <code>eq(k1,k2)</code> then
    <code>c_eq(ck,k2)</code>,</li>
  <li>if <code>c_eq(ck,k1)</code> and <code>c_eq(ck,k2)</code> then
    <code>eq(k1,k2)</code>,</li>
  <li>if <code>c_eq(ck,k1)</code> then <code>c_hash(ck)==hash(k1)</code>,</li>
</ol>
for every <code>c_hash</code> of type <code>CompatibleHash</code>,
<code>c_eq</code> of type <code>CompatiblePred</code>,
<code>hash</code> of type <code>Hash</code>,
<code>eq</code> of type <code>Pred</code>, <code>ck</code> of type
<code>CompatibleKey</code> and <code>k1</code>, <code>k2</code> of type
<code>Key</code>.
</p>

<p>Additionally, a type <code>CompatibleKey</code> is said to be a
<i>compatible key</i> of (<code>Hash</code>, <code>Pred</code>) if
(<code>CompatibleKey</code>, <code>Hash</code>, <code>Pred</code>)
is a compatible extension of (<code>Hash</code>, <code>Pred</code>).
This implies that <code>Hash</code> and <code>Pred</code> accept arguments
of type <code>CompatibleKey</code>, which usually means they have
several overloads of their corresponding <code>operator()</code>
member functions.
</p>

<p>
In the context of a compatible extension or a compatible key, the expression
"equivalent key" takes on its obvious interpretation.
</p>

<code>template&lt;typename CompatibleKey> iterator find(const CompatibleKey&amp; x)const;
</code>

<blockquote>
<b>Requires:</b> <code>CompatibleKey</code> is a compatible key of
(<code>hasher</code>, <code>key_equal</code>).<br>
<b>Effects:</b> Returns a pointer to an element whose key is equivalent to
<code>x</code>, or <code>end()</code> if such an element does not exist.<br>
<b>Complexity:</b> Average case <code>O(1)</code> (constant), worst case
<code>O(n<sub>dist</sub>)</code>.<br>
</blockquote>

<code>template&lt;<br>
&nbsp;&nbsp;typename CompatibleKey,typename CompatibleHash, typename CompatiblePred<br>
&gt;<br>
iterator find(<br>
&nbsp;&nbsp;const CompatibleKey&amp; x,<br>
&nbsp;&nbsp;const CompatibleHash&amp; hash,const CompatiblePred&amp; eq)const;
</code>

<blockquote>
<b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleHash</code>,
<code>CompatiblePred</code>) is a compatible extension of
(<code>hasher</code>, <code>key_equal</code>).<br>
<b>Effects:</b> Returns a pointer to an element whose key is equivalent to
<code>x</code>, or <code>end()</code> if such an element does not exist.<br>
<b>Complexity:</b> Average case <code>O(1)</code> (constant), worst case
<code>O(n<sub>dist</sub>)</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey><br>
size_type count(const CompatibleKey&amp; x)const;
</code>

<blockquote>
<b>Requires:</b> <code>CompatibleKey</code> is a compatible key of
(<code>hasher</code>, <code>key_equal</code>).<br>
<b>Effects:</b> Returns the number of elements with key equivalent to <code>x</code>.<br>
<b>Complexity:</b> Average case <code>O(count(x))</code>, worst case
<code>O(count(x)+n<sub>dist</sub>)</code>.<br>
</blockquote>

<code>template&lt;<br>
&nbsp;&nbsp;typename CompatibleKey,typename CompatibleHash, typename CompatiblePred<br>
&gt;<br>
size_type count(<br>
&nbsp;&nbsp;const CompatibleKey&amp; x,<br>
&nbsp;&nbsp;const CompatibleHash&amp; hash,const CompatiblePred&amp; eq)const;
</code>

<blockquote>
<b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleHash</code>,
<code>CompatiblePred</code>) is a compatible extension of
(<code>hasher</code>, <code>key_equal</code>).<br>
<b>Effects:</b> Returns the number of elements with key equivalent to <code>x</code>.<br>
<b>Complexity:</b> Average case <code>O(count(x,hash,eq))</code>, worst case
<code>O(count(x,hash,eq)+n<sub>dist</sub>)</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey><br>
bool contains(const CompatibleKey&amp; x)const;
</code>

<blockquote>
<b>Requires:</b> <code>CompatibleKey</code> is a compatible key of
(<code>hasher</code>, <code>key_equal</code>).<br>
<b>Effects:</b> Returns <code>true</code> iff there is some element with key equivalent to <code>x</code>.<br>
<b>Complexity:</b> Average case <code>O(1)</code> (constant), worst case
<code>O(n<sub>dist</sub>)</code>.<br>
</blockquote>

<code>template&lt;<br>
&nbsp;&nbsp;typename CompatibleKey,typename CompatibleHash, typename CompatiblePred<br>
&gt;<br>
bool contains(<br>
&nbsp;&nbsp;const CompatibleKey&amp; x,<br>
&nbsp;&nbsp;const CompatibleHash&amp; hash,const CompatiblePred&amp; eq)const;
</code>

<blockquote>
<b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleHash</code>,
<code>CompatiblePred</code>) is a compatible extension of
(<code>hasher</code>, <code>key_equal</code>).<br>
<b>Effects:</b> Returns <code>true</code> iff there is some element with key equivalent to <code>x</code>.<br>
<b>Complexity:</b> Average case <code>O(1)</code> (constant), worst case
<code>O(n<sub>dist</sub>)</code>.<br>
</blockquote>

<code>template&lt;typename CompatibleKey><br>
std::pair&lt;iterator,iterator> equal_range(const CompatibleKey&amp; x)const;
</code>

<blockquote>
<b>Requires:</b> <code>CompatibleKey</code> is a compatible key of
(<code>hasher</code>, <code>key_equal</code>).<br>
<b>Effects:</b> Returns a range containing all elements with keys equivalent
to <code>x</code> (and only those), or (<code>end()</code>,<code>end()</code>)
if no such elements exist.<br>
<b>Complexity:</b> Average case <code>O(1)</code> (constant), worst case
<code>O(n<sub>dist</sub>)</code>.<br>
</blockquote>

<code>template&lt;<br>
&nbsp;&nbsp;typename CompatibleKey,typename CompatibleHash, typename CompatiblePred<br>
&gt;<br>
std::pair&lt;iterator,iterator> equal_range(<br>
&nbsp;&nbsp;const CompatibleKey&amp; x,<br>
&nbsp;&nbsp;const CompatibleHash&amp; hash,const CompatiblePred&amp; eq)const;
</code>

<blockquote>
<b>Requires:</b> (<code>CompatibleKey</code>, <code>CompatibleHash</code>,
<code>CompatiblePred</code>) is a compatible extension of
(<code>hasher</code>, <code>key_equal</code>).<br>
<b>Effects:</b> Returns a range containing all elements with keys equivalent
to <code>x</code> (and only those), or (<code>end()</code>,<code>end()</code>)
if no such elements exist.<br>
<b>Complexity:</b> Average case <code>O(1)</code> (constant), worst case
<code>O(n<sub>dist</sub>)</code>.<br>
</blockquote>

<h4><a name="bucket_interface">Bucket interface</a></h4>

<code>local_iterator&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;local_iterator_to(const value_type&amp; x);<br>
const_local_iterator local_iterator_to(const value_type&amp; x)const;</code>
  
<blockquote>
<b>Requires:</b> <code>x</code> is a reference to an element of the container.<br>
<b>Returns:</b> An iterator to <code>x</code>.<br>
<b>Complexity:</b> Constant.<br>
<b>Exception safety:</b> <code>nothrow</code>.<br>
</blockquote>


<h4><a name="hash_policy">Hash policy</a></h4>

<code>void rehash(size_type n);</code>

<blockquote>
<b>Effects:</b> Increases if necessary the number of internal buckets
so that <code>size()/bucket_count()</code> does not exceed the maximum
load factor, and <code>bucket_count()>=n</code>.<br>
<b>Postconditions:</b> Validity of iterators and references to the
elements contained is preserved.<br>
<b>Complexity:</b> <code>O(m)</code>, where <code>m</code> is the number of
non-equivalent elements in the index.<br>
<b>Exception safety:</b> Strong.
</blockquote>

<code>void reserve(size_type n);</code>

<blockquote>
<b>Effects:</b>
<blockquote><pre>
<span class=identifier>rehash</span><span class=special>(</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>ceil</span><span class=special>(</span><span class=identifier>n</span><span class=special>/</span><span class=identifier>max_load_factor</span><span class=special>()));</span>
</pre></blockquote>
</blockquote>

<h4><a name="comparison">Comparison</a></h4>

<code>template&lt;<i>implementation defined</i>&gt;<br>
bool operator==(const <i>index class name</i>&amp; x,const <i>index class name</i>&amp; y);</code>

<blockquote>
<b>Requires:</b> <code>x.key_extractor()</code>, <code>x.hash_function()</code> and
<code>x.key_eq()</code> have the same behavior as the corresponding objects in <code>y</code>.
For any two elements <code>e1</code>, <code>e2</code> in <code>x</code> or <code>y</code>,
if <code>e1==e2</code> then their keys are equivalent.<br>
<b>Returns:</b> <code>true</code> iff <code>x</code> and <code>y</code> have the same size
and for each key <code>k</code> present in <code>x</code> the range
<code>x.equal_range(k)</code> is equal (considering the <code>==</code> operator of <code>value_type</code>)
to <code>y.equal_range(k)</code> under permutations of the elements.<br>
<b>Complexity:</b> Let <code>k<sub>1</sub></code>,...,<code>k<sub>m</sub></code> be the different
keys present in <code>x</code>:<br>
<ul>
  <li>If, for each <code>k<sub>i</sub></code>, <code>x.equal_range(k<sub>i</sub>)</code> is arranged
    in the same order as <code>y.equal_range(k<sub>i</sub>)</code>, average case is
    <code>O(x.size())</code>, worst case <code>O(x.size()<sup>2</sup>)</code>.
  </li>
  <li>Otherwise, average case is
    <code>O(<font style="font-size:1.5em">&Sigma;</font>(x.count(k<sub>i</sub>)<sup>2</sup>))</code>,
    worst case <code>O(x.size()<sup>2</sup>)</code>.
  </li>
</ul>
(For unique indices, the formulas above reduce to average case 
<code>O(x.size())</code>, worst case <code>O(x.size()<sup>2</sup>)</code>.)
</blockquote>

<h4><a name="serialization">Serialization</a></h4>

<p>
Indices cannot be serialized on their own, but only as part of the
<code>multi_index_container</code> into which they are embedded. In describing
the additional preconditions and guarantees associated to hashed indices
with respect to serialization of their embedding containers, we
use the concepts defined in the <code>multi_index_container</code>
<a href="multi_index_container.html#serialization">serialization section</a>.
</p>

Operation: saving of a <code>multi_index_container</code> <code>m</code> to an
output archive (XML archive) <code>ar</code>.

<blockquote>
<b>Requires:</b> No additional requirements to those imposed by the container.
</blockquote>

Operation: loading of a <code>multi_index_container</code> <code>m'</code> from an
input archive (XML archive) <code>ar</code>.

<blockquote>
<b>Requires:</b> Additionally to the general requirements, the binary predicate
<code><i>value_eq</i>(m'.get&lt;i&gt;())</code> must be serialization-compatible with
<code><i>value_eq</i>(m.get&lt;i&gt;())</code>, where
<code><i>value_eq</i>(c)(x,y)</code> is defined as
<code>c.key_eq()(c.key_extractor()(x),c.key_extractor()(y))</code>
and <code>i</code> is the position of the hashed index in the container.<br>
<b>Postconditions:</b> On successful loading, the range 
[<code>begin()</code>, <code>end()</code>) contains restored copies of every
element in [<code>m.get&lt;i&gt;().begin()</code>, <code>m.get&lt;i&gt;().end()</code>),
though not necessarily in the same order.
</blockquote>

Operation: saving of an <code>iterator</code> or <code>const_iterator</code>
<code>it</code> to an output archive (XML archive) <code>ar</code>.

<blockquote>
<b>Requires:</b> <code>it</code> is a valid iterator of the index. The associated
<code>multi_index_container</code> has been previously saved.
</blockquote>

Operation: loading of an <code>iterator</code> or <code>const_iterator</code>
<code>it'</code> from an input archive (XML archive) <code>ar</code>.

<blockquote>
<b>Postconditions:</b> On successful loading, if <code>it</code> was dereferenceable
then <code>*it'</code> is the restored copy of <code>*it</code>, otherwise
<code>it'==end()</code>.<br>
<b>Note:</b> It is allowed that <code>it</code> be a <code>const_iterator</code>
and the restored <code>it'</code> an <code>iterator</code>, or vice versa.
</blockquote>

Operation: saving of a <code>local_iterator</code> or
<code>const_local_iterator</code>
<code>it</code> to an output archive (XML archive) <code>ar</code>.

<blockquote>
<b>Requires:</b> <code>it</code> is a valid local iterator of the index. The
associated <code>multi_index_container</code> has been previously saved.
</blockquote>

Operation: loading of a <code>local_iterator</code> or
<code>const_local_iterator</code>
<code>it'</code> from an input archive (XML archive) <code>ar</code>.

<blockquote>
<b>Postconditions:</b> On successful loading, if <code>it</code> was dereferenceable
then <code>*it'</code> is the restored copy of <code>*it</code>; if <code>it</code>
was <code>m.get&lt;i&gt;().end(n)</code> for some <code>n</code>, then
<code>it'==m'.get&lt;i&gt;().end(n)</code> (where <code>m</code> is the original
<code>multi_index_container</code>, <code>m'</code> its restored copy
and <code>i</code> is the ordinal of the index.)<br>
<b>Note:</b> It is allowed that <code>it</code> be a <code>const_local_iterator</code>
and the restored <code>it'</code> a <code>local_iterator</code>, or vice versa.
</blockquote>

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<p>Revised March 15th 2024</p>

<p>&copy; Copyright 2003-2024 Joaqu&iacute;n M L&oacute;pez Mu&ntilde;oz.
Distributed under the Boost Software 
License, Version 1.0. (See accompanying file <a href="../../../../LICENSE_1_0.txt">
LICENSE_1_0.txt</a> or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
http://www.boost.org/LICENSE_1_0.txt</a>)
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